A035265 One half of deca-factorial numbers.

1, 12, 264, 8448, 354816, 18450432, 1143926784, 82362728448, 6753743732736, 621344423411712, 63377131187994624, 7098238693055397888, 865985120552758542336, 114310035912964127588352, 16232025099640906117545984, 2467267815145417729866989568, 399697386053557672238452310016

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..320

Index entries for sequences related to factorial numbers.

Formula

2*a(n) = (10*n-8)(!^10) = Product_{j=1..n} (10*j-8).

a(n) = 2^n*A008548(n) where A008548(n) = (5*n-4)(!^5) = Product_{j=1..n} (5*j-4).

E.g.f.: (-1 + (1-10*x)^(-1/5))/2.

a(n) = (Pochhammer(2/10,n)*10^n)/2.

Sum_{n>=1} 1/a(n) = 2*(e/10^8)^(1/10)*(Gamma(1/5) - Gamma(1/5, 1/10)). - Amiram Eldar, Dec 22 2022

Maple

seq( mul(10*j-8, j=1..n)/2, n=1..20); # G. C. Greubel, Nov 11 2019

Mathematica

Table[10^n*Pochhammer[2/10, n]/2, {n, 20}] (* G. C. Greubel, Nov 11 2019 *)

Prog

(PARI) vector(20, n, prod(j=1, n, 10*j-8)/2 ) \\ G. C. Greubel, Nov 11 2019
(Magma) [(&*[10*j-8: j in [1..n]])/2: n in [1..20]]; // G. C. Greubel, Nov 11 2019
(Sage) [product( (10*j-8) for j in (1..n))/2 for n in (1..20)] # G. C. Greubel, Nov 11 2019
(GAP) List([1..20], n-> Product([1..n], j-> 10*j-8)/2 ); # G. C. Greubel, Nov 11 2019

Crossrefs

Cf. A008548, A045757, A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279.

Sequence in context: A295844 A113672 A259269 * A167869 A068271 A068283

Adjacent sequences: A035262 A035263 A035264 * A035266 A035267 A035268

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved